We show how the success of deep learning could depend not only on mathematics but also on physics: although well-known mathematical theorems guarantee that neural networks can approximate arbitrary ...functions well, the class of functions of practical interest can frequently be approximated through “cheap learning” with exponentially fewer parameters than generic ones. We explore how properties frequently encountered in physics such as symmetry, locality, compositionality, and polynomial log-probability translate into exceptionally simple neural networks. We further argue that when the statistical process generating the data is of a certain hierarchical form prevalent in physics and machine learning, a deep neural network can be more efficient than a shallow one. We formalize these claims using information theory and discuss the relation to the renormalization group. We prove various “no-flattening theorems” showing when efficient linear deep networks cannot be accurately approximated by shallow ones without efficiency loss; for example, we show that
n
variables cannot be multiplied using fewer than
2
n
neurons in a single hidden layer.
The success of new scientific areas can be assessed by their potential in contributing to new theoretical approaches and in applications to real-world problems. Complex networks have fared extremely ...well in both of these aspects, with their sound theoretical basis being developed over the years and with a variety of applications. In this survey, we analyze the applications of complex networks to real-world problems and data, with emphasis in representation, analysis and modeling. A diversity of phenomena are surveyed, which may be classified into no less than 11 areas, providing a clear indication of the impact of the field of complex networks.
Seismic waves - generated both by natural earthquakes and by man-made sources - have produced an enormous amount of information about the Earth's interior. In classical seismology, the Earth is ...modeled as a sequence of uniform horizontal layers (or spherical shells) having different elastic properties and one determines these properties from travel times and dispersion of seismic waves. The Earth, however, is not made of horizontally uniform layers, and classic seismic methods can take large-scale inhomogeneities into account. Smaller-scale irregularities, on the other hand, require other methods. Observations of continuous wave trains that follow classic direct S waves, known as coda waves, have shown that there are heterogeneities of random size scattered randomly throughout the layers of the classic seismic model. This book focuses on recent developments in the area of seismic wave propagation and scattering through the randomly heterogeneous structure of the Earth, with emphasis on the lithosphere. The presentation combines information from many sources to present a coherent introduction to the theory of scattering in acoustic and elastic materials and includes analyses of observations using the theoretical methods developed. The second edition especially includes new observational facts such as the spatial variation of medium inhomogeneities and the temporal change in scattering characteristics and recent theoretical developments in the envelope synthesis in random media for the last ten years. Mathematics is thoroughly rewritten for improving the readability. Written for advanced undergraduates or beginning graduate students of geophysics or planetary sciences, this book should also be of interest to civil engineers, seismologists, acoustical engineers, and others interested in wave propagation through inhomogeneous elastic media.
The combined efforts of the Physicists and the Economists in recent years in analyzing and modelling various dynamic phenomena in monetary and social systems have led to encouraging developments, ...generally classified under the title of Econophysics. These developments share a common ambition with the already established field of Quantitative Economics. This volume intends to offer the reader a glimpse of these two parallel initiatives by collecting review papers written by well-known experts in the respective research frontiers in one cover. This massive book presents a unique combination of research papers contributed almost equally by Physicists and Economists. Additional contributions from Computer Scientists and Mathematicians are also included in this volume. The book consists of two parts: the first part concentrates on Econophysics problems and the second part stresses on various quantitative issues in Economics. Both parts specialize on frontier problems in Games and Social Choices.
We introduce a new algorithm for modularity-based community detection in large networks. The algorithm, which we refer to as a smart local moving algorithm, takes advantage of a well-known local ...moving heuristic that is also used by other algorithms. Compared with these other algorithms, our proposed algorithm uses the local moving heuristic in a more sophisticated way. Based on an analysis of a diverse set of networks, we show that our smart local moving algorithm identifies community structures with higher modularity values than other algorithms for large-scale modularity optimization, among which the popular “Louvain algorithm”. The computational efficiency of our algorithm makes it possible to perform community detection in networks with tens of millions of nodes and hundreds of millions of edges. Our smart local moving algorithm also performs well in small and medium-sized networks. In short computing times, it identifies community structures with modularity values equally high as, or almost as high as, the highest values reported in the literature, and sometimes even higher than the highest values found in the literature.
Stochastic energetics is the emerging field that bridges the gap between stochastic dynamical processes and thermodynamics. This book is the first introductory text on the field and gradually takes ...readers from the basics to applications.
Twisted bilayer graphene near the magic angle
exhibits rich electron-correlation physics, displaying insulating
, magnetic
and superconducting phases
. The electronic bands of this system were ...predicted
to narrow markedly
near the magic angle, leading to a variety of possible symmetry-breaking ground states
. Here, using measurements of the local electronic compressibility, we show that these correlated phases originate from a high-energy state with an unusual sequence of band population. As carriers are added to the system, the four electronic 'flavours', which correspond to the spin and valley degrees of freedom, are not filled equally. Rather, they are populated through a sequence of sharp phase transitions, which appear as strong asymmetric jumps of the electronic compressibility near integer fillings of the moiré lattice. At each transition, a single spin/valley flavour takes all the carriers from its partially filled peers, 'resetting' them to the vicinity of the charge neutrality point. As a result, the Dirac-like character observed near charge neutrality reappears after each integer filling. Measurement of the in-plane magnetic field dependence of the chemical potential near filling factor one reveals a large spontaneous magnetization, further substantiating this picture of a cascade of symmetry breaking. The sequence of phase transitions and Dirac revivals is observed at temperatures well above the onset of the superconducting and correlated insulating states. This indicates that the state that we report here, with its strongly broken electronic flavour symmetry and revived Dirac-like electronic character, is important in the physics of magic-angle graphene, forming the parent state out of which the more fragile superconducting and correlated insulating ground states emerge.
The terms phase transitions and phase transformations are often used in an interchangeable manner in the metallurgical literature. In Phase Transformations, transformations driven by pressure ...changes, radiation and deformation and those occurring in nanoscale multilayers are brought to the fore. Order-disorder transformations, many of which constitute very good examples of continuous transformations, are dealt with in a comprehensive manner. Almost all types of phase transformations and reactions that are commonly encountered in inorganic materials are covered and the underlying thermodynamic, kinetic and crystallographic aspects elucidated. * Shows readers the advancements in the field - due to enhanced computing power and superior experimental capability * Drawing upon the background and the research experience of the authors, bringing together a wealth of experience * Written essentially from a physical metallurgists view point
Efficient harnessing of heavy metal pollution is an urgent environmental task. Herein, magnetic bio adsorbent (MB) based on Fe3O4-chitosan-graphene oxide composite was fabricated via one step ...co-precipitation for adsorptive remediation of Cu(II). Remediation efficiency was evaluated by batch adsorption, meanwhile adsorption mechanism was elucidated by spectroscopic tests (XPS, UV–Vis absorption and fluorescent emission spectra), statistical physics formalism, isotherm and kinetic fittings. Results show, MB reaches adsorption percent and quantity of 87.61 % and 350.43 mg·g−1 for Cu(II) in 30 min. By virtue of paramagnetism, MB can be readily recovered with a permanent magnet for easy regeneration and cyclic use, thereby retaining adsorption quantity 279.99 mg·g−1 at the fifth cycle. The Freundlich and pseudo second order model satisfactorily describes the adsorption, designating chemical interaction as the rate limiting step. Statistical physics calculation suggests two points. (1) Multi-ionic adsorption mechanism with exothermic, spontaneous and energy lowering feature. (2) Density of adsorption sites increases with temperature, resulting in improved adsorption capacity. Spectroscopic analysis confirms the involvement of CO, CO, -NH2 in Cu(II) uptake via electron donation. These explorations contribute with novel theoretical illumination for understanding both the thermodynamic feature and atomic scale mechanism of common pollutants adsorption by bio adsorbent like Fe3O4-chitosan-graphene oxide.
Plausible adsorption mechanism of MB on Cu(II) illustrated under the background of Gibbs free energy and adsorption quantity. Blue and violet ball represent MB and Cu(II), respectively. When Ce → 0, only negligible adsorption occurs, thereby inducing little change in Gibbs free energy. In this occasion, violet balls are away from blue ball, depicting negligible adsorption. With the increase of Ce, adsorption proceeds dramatically as to induce remarkable decrease of Gibbs free energy, indicating enhanced spontaneity. In this occasion, violet balls are attached onto blue ball, depicting effective adsorption based on chemical bond, as deciphered by spectroscopic analysis. Chemical bond was labeled behind each interacting pair. Display omitted
•Bio adsorbent (MB) Fe3O4-chitosan-graphene oxide was fabricated to adsorb Cu(II).•Adsorption percent and quantity of 87.61 % and 350.43 mg·g−1 for Cu(II) in 30 min.•Chemical interaction is the rate limiting step of the overall adsorption process.•Multi-ionic, exothermic, spontaneous adsorption determined by statistical physics.•Involvement of CO, CO, -NH2 in Cu(II) uptake via electron donation.
Quantum Plasmas Haas, Fernando
2011, 20110727, 2011-08-28, Letnik:
65
eBook
This book provides an overview of the basic concepts and new methods in the emerging scientific area known as quantum plasmas. In the near future, quantum effects in plasmas will be unavoidable, ...particularly in high density scenarios such as those in the next-generation intense laser-solid density plasma experiment or in compact astrophysics objects. Currently, plasmas are in the forefront of many intriguing questions around the transition from microscopic to macroscopic modeling of charged particle systems. Quantum Plasmas: an Hydrodynamic Approach is devoted to the quantum hydrodynamic model paradigm, which, unlike straight quantum kinetic theory, is much more amenable to investigate the nonlinear realm of quantum plasmas. The reader will have a step-by-step construction of the quantum hydrodynamic method applied to plasmas. The book is intended for specialists in classical plasma physics interested in methods of quantum plasma theory, as well as scientists interested in common aspects of two major areas of knowledge: plasma and quantum theory.In these chapters, the quantum hydrodynamic model for plasmas, which has continuously evolved over the past decade, will be summarized to include both the development and applications of the method.
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